The Australian constitution, in seemingly categorical terms, bar people with dual citizenship from being elected to Parliament. Recently two senators had to resign after discovering they were dual citizens. But it did not stop there. Two further senators may be dual citizens and their case has been referred to the High Court.
And most dramatically, the deputy PM Barnaby Jones is a NZ citizen, as was recently discovered. Barnaby Joyce: NZ confirms Australian deputy PM is dual citizen - BBC News
He is a member of the lower house, the House of Representatives, and if he were forced to resign the Government would lose its majority there. His case has been referred to the High Court as well. The government claims they are confident he won't have to resign since he did not know about his Kiwi citizenship, though that has no support in the constitutional text and only dubious support in case law.
Personally, the rule seems silly to me, and think Australia should abolish it, but so far that looks unlikely.